\newproblem{lay:1_4_39}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.4.39}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Determine if the columns of the following matrix span all $\mathbb{R}^4$
	\begin{center}
		$A=\begin{pmatrix}10 &-7&1&4&6\\-8&4&-6&-10&-3\\-7&11&-5&-1&-8\\3&-1&10&12&12\end{pmatrix}$
	\end{center}
}
{
  % Solution
	By applying row operations we reach
	\begin{center}
		$A\sim\begin{pmatrix}10 &-7&1&4&6\\0&-1.6&-5.2&-6.8&1.8\\0&0&-24.125&-24.125&3.0625\\0&0&0&0&12.215\end{pmatrix}$
	\end{center}
	This latter matrix has 4 pivot columns (1, 2, 3 and 5), therefore, it spans $\mathbb{R}^4$.
}
\useproblem{lay:1_4_39}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
